Archaeopteryx often is referred to as a transitional fossil because its fossils suggest that it is an intermediate organism between dinosaurs and birds. Transitional forms in the fossil record, such as Archaeopteryx, provide evidence for which pattern of evolution

Answer: a. 2(11a+14)

b. 47x-17

c. x^2+5x

d. x(x+8)

Step-by-step explanation:

a. 2a+4(7+5a)=

2a+4*7+4(5a)=

2a+28+20a=

22a+28=2(11a+14)

b. 4(3x+2)-5(7x+5)=

12x+8-35x-25=

12x+35x+8-25=47x-17

c. x(x+5)=x^2+5x

d. 2x+x(x+6)=

2x+x^2+6x=

x^2+8x=x(x+8)

Here are the amounts of weight change (in pounds) for the 12 women:

-1, -3, -8, 7.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

The list represents the amount of weight change (in pounds) for 12 women during their first year of work after graduating from college. The values in the list can be positive or negative. A positive value indicates that a woman gained weight during the year, while a negative value indicates that she lost weight.

Looking at the list, we can see that the first three women lost weight, with weight changes of -1, -3, and -8 pounds respectively. The fourth woman gained weight, with a weight change of 7 pounds, and the fifth woman gained even more weight, with a weight change of 15 pounds.

The sixth woman also gained weight, but only by 3 pounds. The next woman on the list lost weight, with a weight change of -11 pounds, and the following woman lost weight as well, with a weight change of -6 pounds.

The last four women on the list all gained weight. The eighth woman gained 12 pounds, the ninth woman did not experience any weight change, the tenth woman lost 4 pounds, and the final woman on the list lost 11 pounds.

Therefore, Here are the amounts of weight change (in pounds) for the 12 women:-1, -3, -8, 7.

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Correct question is " Listed below are the amounts of weight change (in pounds) for 12 women during their first year of work after graduating from college. Positive values correspond to women who gained weight, and negative values correspond to women who lost weight -1 -3 -8 7 15 3 -11 -6 12 0 -4 -11

Find the amounts of weight change (in pounds) for the 12 women?"

Answer:

i think it's <C and <R since they're 90 degree angles, though they are small

I am sorry but I cannot answer your question with the contained elements.

Answer:

60

Step-by-step explanation:

what am i supposed to answer frl

Answer:

y = -2x + 9

Step-by-step explanation:

The general shape of the equation is y = ax + b, you just have to find a and b.

b is simple, it is the y coordinate where the line crosses the y axis, i.e., b=9.

a is the slope of the line. This is the change in y when you take one step to the right. The change is -2.

Hence y = -2x + 9

To determine from which group the patient with a drop of 22.5 points is more likely to have come from, we need to compare the mean drop in anxiety level for each group. The mean drop in anxiety level for group T is 24.5, for group V is 10.5, and for group C is 2.5.

Since the patient had a drop of 22.5 points, it is more likely that they came from group T, as the drop is closer to the mean drop for group T (24.5) than it is for group V (10.5) or group C (2.5).

Moreover, the fact that the patients in group T were visited by a human volunteer accompanied by a trained dog suggests that they received more attention and support than patients in group V who were visited by a volunteer only or patients in group C who were not visited at all. This may have contributed to the larger drop in anxiety level for group T, making it even more likely that the patient with a drop of 22.5 points came from group T.

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14.3 is probability  of the variance of the number of home runs bautista is projected to hit in 100 games.

How does probability explain work?

Given: n = 100

p = 0.173

Variance = np(1-p)

= 100*0.173*0.827

= 14.3071

Therefore, the variance to two decimal places is

= 14.3.

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Answer:

Step-by-step explanation:

First Selling price is $360, after mark down.

The second's selling price is $403, after both mark downs

Joanne should buy the first, because of the selling price after mark downs.

The inference shows that the author uses paragraph 1 to B. show that science and fun are linked.

An inference simply means the conclusion that can be deduced from the information given on an excerpt.

In this case, the inference shows that the author uses paragraph 1 to show that science and fun are linked. This was illustrated in the story about roller coasters.

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Answer:

The correct answer is B

Step-by-step explanation:

I took this test

Answer:

Step-by-step explanation:

9x^2 + 24x + 16 = 0

(3x + 4)(3x+4)=0

3x + 4 = 0

3x = -4

x = -4/3

3x + 4 = 0

3x = -4

x = -4/3

The number and type of roots of each quadratic function are:

The type of roots of a quadratic function is given by the value of the discriminant, which is the value under the square root of the quadratic formula.

The types of roots of a quadratic equation are;

The roots or solution to the quadratic equation, a·x² + b·x + c = 0, are given by the quadratic formula, \(x = \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}\)

Where:

b² - 4·a·c is known as the discriminant of the quadratic equation.

The type of root of a quadratic equation is given by the discriminant, b² - 4·a·c, as follows:

The given functions are:

Comparing the above equation to the, general form of a quadratic equation, f(x) = a·x² + b·x + c, we have;

a = 1, b = -9, and c = 21

The discriminant is therefore, (-9)² - 4 × 1 × 21 = -3 < 0

The quadratic equation therefore, has complex roots.

The quadratic equation, f(x) = x² + 16·x - 64 has a discriminant given as follows;

The discriminant is: 16² - 4 × 1 × (-64) = 512 > 0, therefore, the quadratic equation two real roots, given by the equation;

\(x = \dfrac{-16\pm \sqrt{16^2 - 4\times 1 \times 64} }{2\times 1}= \dfrac{-16\pm \sqrt{512} }{2}= \dfrac{-16\pm 16\cdot \sqrt{2} }{2}\)

x = -8 + 8·√2 or x = -8 - 8·√2

The value of the discriminant is 10² - 4 × (-4) × 84 = 1444 > 0, therefore, the equation has two real and distinct roots, given by the equation;\(x = \dfrac{-10\pm \sqrt{1444} }{2\times (-4)}= \dfrac{-10\pm 38 }{-8}\)

\(x = \dfrac{28 }{-8}= -3.5\) and \(x = \dfrac{-48 }{-8}= 6\)

The discriminant of the above quadratic equation is; 0² - 4 × 3 ×24 = -288 < 0

Therefore, the quadratic equation, f(x) = 3·x² + 24, has no real roots or complex roots

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Answer:

x= 1/28+y + 11/84

Step-by-step explanation:

The area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10 is 174/3 units².

To find the area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10, we need to solve this problem in the following way:

Since the curves are already in the form of x = f(y), we need to use vertical strips to find the area.

So, the integral for the area of the region is given by:

A = ∫a b [x₂(y) - x₁(y)] dy

Here, x₂(y) = 10 - 2y² - 12y - 19/5 = - 2y² - 12y + 1/2 and x₁(y) = -4y - 10

So,

A = ∫(-3)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy + ∫(-2)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy

=> A = ∫(-3)⁻²[2y² + 8y - 19/2] dy + ∫(-2)⁻²[2y² + 8y - 19/2] dy

=> A = [(2/3)y³ + 4y² - (19/2)y]₋³ - [(2/3)y³ + 4y² - (19/2)y]₋² | from y = -3 to -2

=> A = [(2/3)(-2)³ + 4(-2)² - (19/2)(-2)] - [(2/3)(-3)³ + 4(-3)² - (19/2)(-3)]

=> A = 174/3

Hence, the area of the region enclosed by the curves is 174/3 units².

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"a lawyer researched the average number of years served by 45 different justices on the supreme court. the average number of years served was 13.8 years with a standard deviation of 7.3 years.

The 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].According to the central limit theorem , a sampling distribution of the means is usually distributed in a normal distribution, given a big enough sample size, which means that it has a bell-shaped curve. It has a standard deviation that can be estimated by dividing the population standard deviation by the square root of the sample size. Using the formula below,

we can calculate the 95% confidence interval for the population average.= 13.8 ± (1.96 × 7.3 / √45)

= 13.8 ± (1.96 × 1.088)

= 13.8 ± 2.13The limits are calculated by adding and subtracting the calculated value from the sample mean.13.8 + 2.13

= 15.9313.8 - 2.13

= 11.67Therefore, the 95% confidence interval estimate for the average number of years served by all supreme court justices is [11.2, 16.4].

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Answer: \(10.72\ cm\)

Step-by-step explanation:

Given

Radius of circle \(r=14\ cm\)

Length of chord is \(l=18\ cm\)

Suppose the distance between the chord and center is x

From figure, we can write

\(\Rightarrow r^2=x^2+9^2\\\Rightarrow 14^2=x^2+9^2\\\Rightarrow x^2=196-81\\\Rightarrow x^2=115\\\Rightarrow x=\sqrt{115}\\\Rightarrow x=10.72\ cm\)

Answer:

1. x2-2x-24=0

break middle term

= x2-6x+4x-24=0

factorise:

x(x-6)+4(x-6)=0

=(x+4)(x-6)=0

x+4=0

x= -4

x-6=0

x= 6

2. x2-11x+18=0

break middle term

x2-9x-2x+18=0

Factorise

x(x-9)-2(x-9)=0

(x-2)(x-9)=0

x-2=0

x=2

x-9=0

x=9

Ask me if u don't know how to break middle term

The correct answer is option d. The theoretical Probability of spinning a multiple of 3 with one spin is 0.

The theoretical probability of an event, we need to identify the number of favorable outcomes (the desired event) and the total number of possible outcomes.

In this case, the event is spinning a multiple of 3 on the spinner. Let's examine the possible outcomes and identify the favorable outcomes:

Possible outcomes on the spinner: {1, 2, 3, 4, 5, 6}

Favorable outcomes (multiples of 3): {3, 6}

The total number of possible outcomes is 6, and the number of favorable outcomes is 2.

The theoretical probability of spinning a multiple of 3 can be calculated as:

P(multiple of 3) = (Number of favorable outcomes) / (Total number of possible outcomes)

P(multiple of 3) = 2 / 6

Simplifying the fraction, we get:

P(multiple of 3) = 1 / 3

Therefore, the correct answer is option d. The theoretical probability of spinning a multiple of 3 with one spin is 0.

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Answer:

30.4%

Step-by-step explanation:

Given data

originally price $457

new price= $318

Required

The percent mark down

Percent markdown= original- new/original*100

substitute

Percent markdown= 457- 318/457*100

Percent markdown= 139/457*100

Percent markdown=0.304*100

Percent markdown=30.4%

Hence the price was reduced by 30.4%

To find the endpoints of the latus rectum of the given parabola, we need to consider the equation in the standard form:

4p(x - h) = (y - k)^2

where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus and the directrix.

Given the equation: (x^2) = 120(y - 1)^2

Comparing it with the standard form, we have:

4p = 120

Simplifying:

p = 30

The vertex of the parabola is at (h, k) = (0, 1).

Since the latus rectum is the line segment passing through the focus and perpendicular to the axis of symmetry, it has a length of 4p.

Therefore, the endpoints of the latus rectum are located at (0, 1 ± p), which gives us:

Endpoint 1: (0, 1 + 30) = (0, 31)

Endpoint 2: (0, 1 - 30) = (0, -29)

Hence, the endpoints of the latus rectum of the given parabola are (0, 31) and (0, -29).

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Answer:

The Symmetric Property states that for all real numbers a and b, if a=b, then b=a.

Thus, we conclude that the property used here is the symmetric property of equality.

Step-by-step explanation:

Given that

if 5 = 3x - 4, then 3x - 4= 5

Thus, we conclude that the property used here is the symmetric property of equality.

CHECKING

Subtituting x = 3

5 = 3(3)-4

5 = 5

also

3x - 4= 5

3(3)-4 = 5

5=5

Thus,

The requried area of the board is 110 square feet, option D is correct.

From the figure,

The length of the board is 11 feet
The width of the board is 10 feet

The area of the board is given as:

Area = length x width
Area = 11 × 10
Area = 110 square feet.

Thus, the requried area of the board is 110 square feet, and option D is correct.

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495.95

convert the percentage into a decimal

0.09

then do b=1-r

1 - 0.09 = 0.91

Now do 545 x 0.91

Answer: 495.95

Let's assume that the original price of the antique was x.

We know that the antique was sold at a profit of 9%, which means that the selling price is 109% of the original price:

\(Selling \: price = Original \: price + Profit\)

\(£545 = x + 0.09x \\ £545 = 1.09x\)

\(x = 500\)

Answer:

74 degrees

Step-by-step explanation:

As sum of interior and exterior at a vertex add to 180, subtract 106 from 180 to get 74 degrees

Answer:

length = 5

Step-by-step explanation:

area = length × width

23 = length × 4.6

23 ÷ 4.6 = length

5 = length

On average, you can expect to get about 4.24 points per game if you play many times.

To find the average number of points you can get by playing the game many times, you can use the expected value as a guide.

The expected value of the game is calculated as follows:

(20 points x probability of getting 20) + (10 points x probability of getting 10) + (2 points x probability of getting 2) = 5.6

Let's use the variables p20, p10, and p2 to represent the probabilities of getting 20 points, 10 points, and 2 points, respectively. Then we can set up the equation:

(20p20) + (10p10) + (2p2) = 5.6

We also know that the sum of the probabilities must equal 1:

p20 + p10 + p2 = 1

Now we have two equations and three variables. We need one more equation to solve for the variables. One way to do this is to assume that the probabilities of getting 20 points, 10 points, and 2 points are proportional to the point values themselves.

In other words, let's assume that:

p20 : p10 : p2 = 20 : 10 : 2

We can then use this proportion to write p20 and p2 in terms of p10:

p20 = 2p10

p2 = 4p10

Now we can substitute these expressions into the two equations we have:

(20p20) + (10p10) + (2p2) = 5.6

p20 + p10 + p2 = 1

Substituting the first equation gives:

(20(2p10)) + (10p10) + (2(4p10)) = 5.6

Simplifying:

80p10 + 10p10 = 5.6

90p10 = 5.6

p10 = 5.6/90

p10 = 0.062

Now we can use the proportions to find p20 and p2:

p20 = 2p10 = 2(0.062) = 0.124

p2 = 4p10 = 4(0.062) = 0.248

Finally, we can calculate the average number of points:

(20 points x 0.124) + (10 points x 0.062) + (2 points x 0.248) = 3.12 + 0.62 + 0.496 = 4.236

So, on average, you can expect to get about 4.24 points per game if you play many times.

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The horizontal distance between the plane and the airport can be found to be approximately 4, 602 feet.

To solve this problem, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle of elevation, the horizontal distance, and the altitude in a right triangle.

Let x be the horizontal distance between the plane and the airport. We can set up the following equation using the tangent function:

tan(θ) = opposite side / adjacent side

tan(41°) = 4000 ft / x

Now, we can solve for x:

x = 4000 ft / tan(41°)

x ≈ 4000 ft / 0.8693 (rounded to 4 decimal places)

x ≈ 4601.68 ft

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The amount the firm needs to deposit in the account now is 9,640.11. Given that the company has purchased a life truck with a useful life of 5 years, the maintenance costs for the truck during the first year are 2,000.

Also, maintenance costs are expected to increase at a rate of 300 per year over the remaining life, which is for four years. Assume that the maintenance costs occur at the end of each year.

The future maintenance costs for the truck can be calculated as shown below:

Year 1:\($2,000Year 2: $2,300Year 3: $2,600Year 4: $2,900Year 5: $3,200\)The maintenance account that earns 10% interest per year has to be set up, and all future maintenance expenses will be paid out of this account. The future value of the maintenance costs, i.e., the amount that the firm needs to deposit now to earn 10% interest and pay the maintenance costs over the next four years is given by:

\(PV = [C/(1 + i)] + [C/(1 + i)²] + [C/(1 + i)³] + [C/(1 + i)⁴] + [(C + FV)/(1 + i)⁵]\),where PV is the present value of the future maintenance costs, C is the annual maintenance cost, i is the interest rate per year, FV is the future value of the maintenance costs at the end of year 5, which is $3,200, and 5 is the total number of years, which is

5.Substituting the given values in the above equation:

\(PV = [2,000/(1 + 0.1)] + [2,300/(1 + 0.1)²] + [2,600/(1 + 0.1)³] + [2,900/(1 + 0.1)⁴] + [(3,200 + 3,200)/(1 + 0.1)⁵] = 9,640.11\)Therefore, the firm needs to deposit 9,640.11 in the account now. Hence, option (A) is the correct answer.

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Answer:

x = 35/9 or 3 8/9

Step-by-step explanation:

removing the fractions implies using the distributive property, which is multiplying each term outside the parentheses by each term inside

in this problem, after distributing 3/5 we get:

3/5x - 3 = -2/3

we want to isolate the 'x' so we undo subtraction first by adding 3 to each side to get:

3/5x = 9/3 - 2/3

3/5 x = 7/3

x = 7/3 × 5/3

x = 35/9

3/5x = 7/3

we can get the 'x' by itself if we multiply each side by the reciprocal of 3/5, which is 5/3 to get:

x = 7/3 × 5/3

x = 35/3